Preview

Features

Well-written and comprehensive introduction to theory of Bayesian statistics

Each of the introductory chapters begins by introducing one new concept or assumption

Uses "just-in-time mathematics"—the introduction to mathematical ideas just before they are applied

Each chapter ends with a summary and exercises

Summary

An intuitive and mathematical introduction to subjective probability and Bayesian statistics.

An accessible, comprehensive guide to the theory of Bayesian statistics, Principles of Uncertainty presents the subjective Bayesian approach, which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. Both rigorous and friendly, the book contains:

Introductory chapters examining each new concept or assumption

Just-in-time mathematics – the presentation of ideas just before they are applied

Summary and exercises at the end of each chapter

Discussion of maximization of expected utility

The basics of Markov Chain Monte Carlo computing techniques

Problems involving more than one decision-maker

Written in an appealing, inviting style, and packed with interesting examples, Principles of Uncertainty introduces the most compelling parts of mathematics, computing, and philosophy as they bear on statistics. Although many books present the computation of a variety of statistics and algorithms while barely skimming the philosophical ramifications of subjective probability, this book takes a different tack. By addressing how to think about uncertainty, this book gives readers the intuition and understanding required to choose a particular method for a particular purpose.

Table of Contents

ProbabilityAvoiding being a sure loserDisjoint events Events not necessarily disjoint Random variables, also known as uncertain quantities Finite number of values Other properties of expectation Coherence implies not a sure loser Expectations and limits

Author(s) Bio

Reviews

This book mainly focuses on the use of Bayesian statistics. It is written using stories and many examples to which readers can relate, and is thus an engaging and appealing text on what is generally a very dry mathematical subject.—John J. Shea, IEEE Electrical Insulation Magazine, May/June 2013, Vol. 29, No. 3

This text provides a unique blend of theory, methods, philosophy and applications that is suitable for a course in Bayesian probability and statistics. … provides thought-provoking material for teaching. …—Erkki P. Liski, International Statistical Review, 2012

In this remarkable book, Kadane begins at the most rudimentary level, develops all the needed mathematics on the fly, and still manages to flesh out at least the core of the whole story, slowly, thoughtfully, and rigorously, right up to graduate level. Major theorems all proved in detail appear here, but not for their own sake; the author always carefully selects them to clarify the basic meaning of the subject and his own views concerning the pitfalls and subtleties of its proper application. Summing Up: Highly recommended.—D.V. Feldman, CHOICE, February 2012

Principles of Uncertainty is a profound and mesmerising book on the foundations and principles of subjectivist or behaviouristic Bayesian analysis. … the book is a pleasure to read. And highly recommended for teaching as it can be used at many different levels. … A must-read for sure!—Christian Robert, The Statistics Forum/CHANCE, October 2011

It's a lovely book, one that I hope will be widely adopted as a course textbook.—Michael Jordan, University of California, Berkeley, USA

A careful, complete, and lovingly written exposition of the subjective Bayesian viewpoint by one of its most eloquent and staunch defenders. Summarizes a lifetime of theory, methods, and application developments for the Bayesian inferential engine. A must-read for anyone looking for a deep understanding of the foundations of Bayesian methods and what they offer modern statistical practice.—Bradley P. Carlin, Professor and Head of Division of Biostatistics, University of Minnesota, Minneapolis, USA